Geodesic
CLASSIFICATION OF POLARIZED SYMPLECTIC AUTOMORPHISMS OF FANO VARIETIES OF CUBIC FOURFOLDS
Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 17-37

Voir la notice de l'article provenant de la source Cambridge University Press

We classify the polarized symplectic automorphisms of Fano varieties of smooth cubic fourfolds (equipped with the Plücker polarization) and study the fixed loci. 
FU, LIE. CLASSIFICATION OF POLARIZED SYMPLECTIC AUTOMORPHISMS OF FANO VARIETIES OF CUBIC FOURFOLDS. Glasgow mathematical journal, Tome 58 (2016) no. 1, pp. 17-37. doi: 10.1017/S001708951500004X
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[1] 1.Beauville, A., Some remarks on Kähler manifolds with c_1 = 0, Classification of algebraic and analytic manifolds (Katata, 1982), Progr. Math., vol. 39 (Birkhäuser Boston, Boston, MA, 1983), 1–26. MR728605 (86c:32031). Google Scholar

[2] 2.Beauville, A., Variétés Kähleriennes dont la première classe de Chern est nulle, J. Differ. Geom. 18 (4) (1983), 755–782 (1984). MR 730926 (86c:32030). Google Scholar | DOI

[3] 3.Beauville, A., Antisymplectic involutions of holomorphic symplectic manifolds, J. Topol. 4 (2) (2011), 300–304. MR 2805992 (2012e:53083). Google Scholar | DOI

[4] 4.Beauville, A. and Donagi, R., La variété des droites d'une hypersurface cubique de dimension 4, C. R. Acad. Sci. Paris Sér. I Math. 301 (14) (1985), 703–706. MR 818549 (87c:14047) Google Scholar

[5] 5.Boissière, S., Automorphismes naturels de l'espace de Douady de points sur une surface, Canad. J. Math. 64 (1) (2012), 3–23. MR 2932167 Google Scholar | DOI

[6] 6.Boissière, S., Nieper-Wißkirchen, M. and Sarti, A., Higher dimensional Enriques varieties and automorphisms of generalized Kummer varieties, J. Math. Pures Appl. 95 (5) (2011), 553–563. MR 2786223 (2012g:14070). Google Scholar | DOI

[7] 7.Boissière, S. and Sarti, A., A note on automorphisms and birational transformations of holomorphic symplectic manifolds, Proc. Amer. Math. Soc. 140 (12) (2012), 4053–4062. MR 2957195 Google Scholar | DOI

[8] 8.Camere, C., Symplectic involutions of holomorphic symplectic four-folds, Bull. Lond. Math. Soc. 44 (4) (2012), 687–702. MR 2967237. Google Scholar | DOI

[9] 9.Charles, F., A remark on the Torelli theorem for cubic fourfolds, preprint, arXiv:1209.4509. Google Scholar

[10] 10.Donovan, P., The Lefschetz-Riemann-Roch formula, Bull. Soc. Math. France 97 (1969), 257–273. MR 0263834 (41 #8433). Google Scholar | DOI

[11] 11.Fu, L., On the action of symplectic automorphisms on the CH_0-groups of some hyper-Kähler fourfolds, Mathematische Zeitschrift, DOI: 10.1007/s00209-015-1424-9. (2015). Google Scholar | DOI

[12] 12.González-Aguilera, V. and Liendo, A., Automorphisms of prime order of smooth cubic n-folds, Arch. Math. (Basel) 97 (1) (2011), 25–37. MR 2820585 (2012g:14071). Google Scholar | DOI

[13] 13.Kawatani, K., On the birational geometry for irreducible symplectic 4-folds related to the Fano schemes of lines, preprint, arXiv:0906.0654. Google Scholar

[14] 14.Kontogeorgis, A., Automorphisms of Fermat-like varieties, Manuscr. Math. 107 (2) (2002), 187–205. MR 1894739 (2003a:14043). Google Scholar | DOI

[15] 15.Mongardi, G., Automorphisms of hyperkähler manifolds, Ph.D. thesis (University of RomaTRE, 2013). Google Scholar

[16] 16.Mongardi, G., On symplectic automorphisms of hyper-Kähler fourfolds of K3[2] type, Michigan Math. J. 62 (3) (2013), 537–550. MR 3102529. Google Scholar | DOI

[17] 17.Namikawa, Y., Deformation theory of singular symplectic n-folds, Math. Ann. 319 (3) (2001), 597–623. MR 1819886 (2002b:32025). Google Scholar | DOI

[18] 18.Nikulin, V. V., Finite groups of automorphisms of Kählerian K3 surfaces, Uspehi Mat. Nauk. 31 (2(188)) (1976), 223–224. MR 0409904. Google Scholar

[19] 19.Shioda, T., Arithmetic and geometry of Fermat curves, Algebraic Geometry Seminar (Singapore, 1987), (World Sci. Publishing, Singapore, 1988), 95–102. MR 966448 (90a:11037). Google Scholar

[20] 20.Voisin, C., Hodge theory and complex algebraic geometry. II, Cambridge Studies in Advanced Mathematics, vol. 77 (Cambridge University Press, Cambridge, 2003), Translated from the French by Leila Schneps. MR 1997577 (2005c:32024b). Google Scholar | DOI

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